Diana is making smoothie using bananas, cantaloupes, and milk. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Diana uses: Ingredient Price per kilogram Amount Bananas $0.55$ dollars per kilogram $x$ kilograms Cantaloupes $y$ dollar per kilogram $1.2$ kilograms Milk $z$ dollars per liter $p$ liters The total cost of the ingredients is $2$ dollars. Write an equation that relates $x$, $y$, $z$, and $p$.
Let's find the amount of money Diana spends on each ingredient. Then we can add all these up to represent the total sum. For example, bananas costs $0.55$ dollars per kilogram and Diana uses $x$ kilograms of them, so Diana spends $0.55x$ dollars on bananas: $\begin{aligned} &\phantom{=}\left(0.55\,\dfrac{\text{dollars}}{\text{kilogram}}\right)\left(x\,\text{kilograms}\right) \\\\ &=0.55\cdot x\,\dfrac{\text{dollars}}{\cancel\text{kilogram}}\cdot\,\cancel\text{kilograms} \\\\ &=0.55x\,\text{dollars} \end{aligned}$ Similarly, Diana spends $1.2y$ dollars on cantaloupes and $z\cdot p$ dollars on milk. Ingredient Price per kilogram Amount ${\text{Price}}$ Bananas $0.55$ dollars per kilogram $x$ kilograms ${0.55x\text{ dollars}}$ Cantaloupes $y$ dollar per kilogram $1.2$ kilograms ${1.2y\text{ dollars}}$ Milk $z$ dollars per liter $p$ liters ${zp\text{ dollars}}$ The total amount Diana spends on ingredients, $2$ dollars, is the sum of the prices of each ingredient: $2=0.55x+1.2y+zp$